Metric System Basics

Metric System• The metric system is based on a base

unit that corresponds to a certain kind of measurement

• Length = meter• Volume = liter• Weight (Mass) = gram

• Prefixes plus base units make up the metric system – Example:

• Centi + meter = Centimeter• Kilo + liter = Kiloliter

Prefix Symbol Factor Number Factor Word

Kilo- k 1000 Thousand

Hecto- h 100 HundredDeca- da or dk 10 TenUnit m, l, or g 1 OneDeci- d .1 TenthCenti- c .01 HundredthMilli- m .001 thousandth

Metric UnitsThe metric system has prefix modifiers that are

multiples of 10.

Metric System• The three prefixes that we will use

the most are:– kilo– centi– milli

kilo hecto deca

Base Units

meter

gramliter

deci centi milli

Metric System• So if you needed to measure

length you would choose meter as your base unit– Length of a tree branch

• 1.5 meters – Length of a room

• 5 meters – Length of a ball of twine stretched out

• 25 meters

Metric System• But what if you need to measure a

longer distance, like from your house to school?– Let’s say you live approximately 10

miles from school• 10 miles = 16093 meters

– 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage:• 16093 meters = 16.093 kilometers (or

16.1 if rounded to 1 decimal place)

Metric System• These prefixes are based on powers of

10. What does this mean?– From each prefix every “step” is either:

• 10 times larger or

• 10 times smaller– For example

• Centimeters are 10 times larger than millimeters• 1 centimeter = 10 millimeters

kilo hecto deca

Base Unitsmetergramliter

deci centi milli

Metric System– Centimeters are 10 times

larger than millimeters so it takes more millimeters for the same length

1 centimeter = 10 millimetersExample not to scale

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 mm

1 cm

40

41

41

40

Metric System• For each “step” to right,

you are multiplying by 10• For example, let’s go from a base unit to centi

1 liter = 10 deciliters = 100 centiliters

2 grams = 20 decigrams = 200 centigrams

kilo hecto decameterliter

gramdeci centi milli

( 1 x 10 = 10) = (10 x 10 = 100)

(2 x 10 = 20) = (20 x 10 = 200)

Metric System• An easy way to move within the metric

system is by moving the decimal point one place for each “step” desiredExample: change meters to centimeters

1 meter = 10 decimeters = 100 centimetersor1.00 meter = 10.0 decimeters = 100. centimeters

kilo hecto decameterliter

gramdeci centi milli

Metric System• Now let’s try our previous example from

meters to kilometers:16093 meters = 1609.3 decameters = 160.93

hectometers = 16.093 kilometers• So for every “step” from the base unit to kilo,

we moved the decimal 1 place to the left (the same direction as in the diagram below)

kilo hecto decameterliter

gramdeci centi milli

Metric System• If you move to the left in the diagram,

move the decimal to the left

• If you move to the right in the diagram, move the decimal to the right

kilo hecto decameterliter

gramdeci centi milli

Metric System• Now let’s start from centimeters and

convert to kilometers

400000 centimeters = 4 kilometers

400000 centimeters = 4.00000 kilometers

kilo hecto decameterliter

gramdeci centi milli

Metric System• Now let’s start from kilometers and convert

to millimeters

4 kilometers = 4000000 millimetersor

4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters

kilo hecto decameterliter

gramdeci centi milli

Metric System• Summary

– Base units in the metric system are meter, liter, gram

– Metric system is based on powers of 10– For conversions within the metric system, each

“step” is 1 decimal place to the right or left– Using the diagram below, converting to the right,

moves the decimal to the right and vice versa

kilo hecto decameterliter

gramdeci centi milli